Abstract

The present section will focus on the applicability issues of Monte Carlo-based methods, as well as those methods based on sampling techniques. Special focus will be put on the Multi-Level Monte Carlo method and the two implementations developed during the UMRIDA project, namely the Continuous MLMC and MLMC. All named methods have been described in the above sections of this book.

Abstract

The basic principle of robust parameter design (RPD) is to determine the optimal values of a set of controllable parameters that minimize the quality performance fluctuations caused by noise factors. The dual response surface method is one of the most widely applied approaches in RPD that tries to simultaneously minimize the deviation of the process mean from target and the process variance. However, there are situations when a compromise between the process mean and process variance is necessary, then the trade-off between them becomes an intractable problem. In order to solve the problem, we introduce a method that attempts to integrate the bargaining game theory concept into RPD to determine the optimal solutions. To verify the efficiency of our proposed method, the lexicographic weighted Tchebycheff method is applied to identify if the calculated solution is on the associated Pareto frontier. Two numerical examples show that our model works well in convex frontier cases. Lastly, several sensitivity analyses are conducted to examine the effect of the disagreement point value on the final solution.